Heat oven to 180C/160C fan/gas 4 and pop in a baking sheet to heat up. Use a little of the oil to lightly grease an 18 x 25cm tart tin (ours was 3cm deep). Line the tin with a few strips of baking parchment – this will help you to lift out the tart later.
Unfold the pastry, but keep it covered with a damp tea towel as you work to prevent it from drying out. Taking 1 sheet at a time, brush each piece well with oil, then use to line your tart tin, leaving a little pastry hanging over the edges. Sprinkle a thin layer of breadcrumbs between each layer of pastry as you go – this will help to keep the pastry crisp. When you get to the final layer, brush with a little extra oil and scrunch the edges together to create a pretty border.
Toss the asparagus and courgettes with seasoning and the remaining oil and tip onto a baking tray. Place the pastry case on the top shelf of the oven, with the veg on the shelf below and cook for 10 mins.
Remove the veg from the oven. Brush the tart with a little beaten egg and bake for a further 5 mins until the pastry is golden brown and crunchy.
Whisk the remaining egg with the lemon zest, herbs, crème fraîche and seasoning. Lay half the veg in the bottom of the pastry case and add half the feta. Pour over the egg mixture, then top with the remaining veg and feta. Bake for 40 mins until the filling has set. Remove from the oven and leave to cool. Serve with a grinding of black pepper and scattered with small salad leaves or herbs, if you like.